Top panels: multipolar moments spectra (normalised by random profiles) for the annulus 0.25 ≤ R/R_vir< 0.5 (left) and 1 ≤ R/R_vir< 4 (right) at redshift z = 0 as a function of halo mass. In the internal region, the quadrupole prevails, and reflects the ellipsoidal symmetry of the core. In the external region, the residual power excess at 2 <m< 10, not predicted by GRF approximation, should represent the non-linear sharpening of the filamentary structure. Bottom panels: multipolar moments spectra (normalised by random profiles) for the annulus 0.25 ≤ R/R_vir< 0.5 (left) and 1 ≤ R/R_vir< 4 (right) for the 100 most massive haloes for the z = 0, z ~ 0.3, z ~ 0.6 and z ~ 0.9 simulation outputs. Comparing a population of haloes with the same level of non-linearity (or the same rareness), the shape of haloes appears to be settled early in the cosmic history.